Groups of Low and High Symmetry

Determine whether the molecule belongs to one of the special cases of low or high symmetry. 

inspection of the molecule will determine if it fits one of the low-symmetry cases. These groups have few or no symmetry operations and are described in Table 4-2. 

CHFClBr has no symmetry other than the identity operation and has Q symmetry, H2C = CClBr has only one mirror plane and symmetry, and HClBrC—CHClBr in 

Molecules with many symmetry operations may fit one of the high-symmetry cases of linear, tetrahedral, octahedral, or icosahedral symmetry with the characteristics described in Table 4-3. Molecules with very high symmetry are of two types, linear and polyhedral. Linear molecules having a center of inversion have symmetry those lacking an inversion center have Cx,v symmetry. The highly symmetric point groups Td,Oh, and 4 are described in Table 4-3. It is helpful to note the C axes of these molecules. Molecules with symmetry have only C3 and C2 axes those with Of, symmetry have C4 axes in addition to C3 and C2 and 4 molecules have C5, C3, and C2 axes. 

These molecules are linear, with an infinite number of rotations and an infinite number of reflection planes containing the rotation axis. They do not have a center of inversion. 

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